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NIST Special Publication 1200-21
Characterization of nanoparticle suspensions
using single particle inductively coupled plasma
mass spectrometry
Version 1.0
K. E. Murphy
J. Liu
A. R. Montoro Bustos
M. E. Johnson
M. R. Winchester
This publication is available free of charge from:
http://dx.doi.org/10.6028/NIST.SP.1200-21
NIST Special Publication 1200-21
Characterization of nanoparticle suspensions
using single particle inductively coupled plasma
mass spectrometry
Version 1.0
K. E. Murphy
A. R. Montoro Bustos
M. E. Johnson
M. R. Winchester Chemical Sciences Division
Material Measurement Laboratory
J. Liu Material Measurement Science Division
Material Measurement Laboratory
This publication is available free of charge from:
http://dx.doi.org/10.6028/NIST.SP.1200-21
December 2015
U.S. Department of Commerce Penny Pritzker, Secretary
National Institute of Standards and Technology
Willie May, Under Secretary of Commerce for Standards and Technology and Director
Certain commercial entities, equipment, or materials may be identified in this
document in order to describe an experimental procedure or concept adequately.
Such identification is not intended to imply recommendation or endorsement by the
National Institute of Standards and Technology, nor is it intended to imply that the
entities, materials, or equipment are necessarily the best available for the purpose.
National Institute of Standards and Technology Special Publication 1200-21
Natl. Inst. Stand. Technol. Spec. Publ. 1200-21, 29 pages (December 2015)
CODEN: NSPUE2
This publication is available free of charge from:
http://dx.doi.org/10.6028/NIST.SP.1200-21
ii
FOREWORD
This National Institute of Standards and Technology (NIST) special publication (SP) is one in a
series of NIST SPs that address research needs articulated in the National Nanotechnology
Initiative (NNI) Environmental, Health, and Safety Research Strategy published in 2011 [1].
This Strategy identified a Nanomaterial Measurement Infrastructure (NMI) as essential for
science-based risk assessment and risk management of nanotechnology-enabled products as
pertaining to human health, exposure, and the environment. NIST was identified as the lead
federal agency in the NMI core research area of the Strategy; this research area includes
measurement tools for the detection and characterization of nanotechnology-enabled products.
Single particle inductively coupled plasma mass spectrometry (spICP-MS) is emerging as a
promising analytical method for the characterization of nanoparticles (NPs) in natural matrices at
environmentally relevant concentrations. The rapid development of spICP-MS for counting and
sizing of NPs has resulted in a wide range of recommended metrological conditions for use in the
implementation of this method.
The objective of this SP is to establish a protocol for the determination of mean nanoparticle size
(equivalent spherical particle diameter), number based size distribution, particle number
concentration and mass concentration of ions in an aqueous suspension of NPs using spICP-MS.
The example presented in this SP pertains to the measurement of gold nanoparticles (AuNPs)
and silver nanoparticles (AgNPs), but the presented protocol is applicable to the measurement of
all spherical nanoparticles containing elements measureable by ICP-MS. In addition, this
protocol describes a Kragten spreadsheet approach for estimation of the expanded uncertainty of
the spICP-MS particle size and particle number concentration measurement.
As the method advances, improvements will be realized and updates to this protocol may be
released in the future. Visit http://www.nist.gov/mml/nanoehs-protocols.cfm to check for
revisions and additions to this protocol or for new protocols in the series. We also encourage
users to report citations to published work in which this protocol has been applied.
1
1. Introduction
Fundamental to the study of environmental and human health effects of engineered
nanomaterials (ENMs) is the ability to characterize the material properties of the ENMs used in
the studies within a dose range and in media commensurate with realistic exposure scenarios.
Many of the traditional methods for characterizing nanoparticles (NPs) do not have the capability
to perform the “in situ” measurements required to establish an accurate assessment of the
potential hazards associated with ENMs. Single particle detection using inductively coupled
plasma mass spectrometry (spICP-MS) is a sensitive and selective method capable of direct
analysis of individual NPs in suspension and which can simultaneously provide information on
size, size distribution, particle number concentration, aggregation state, and ionic content.
2. Principles and Scope
The theoretical basis for spICP-MS was first outlined by Degueldre et al. [2]. Measurements
are performed on commercially available ICP-MS instruments and are acquired in time resolved
mode using short (micro second to millisecond), consecutive, measurement periods referred to as
dwell times (tdwell). spICP-MS relies on the principle that as a NP suspended in a solution is
atomized and ionized in the plasma, it will produce a spatially concentrated packet of ions which
is measured as a transient signal spike superimposed on the steady-state signal produced by any
dissolved analyte. The intensity of the transient signal from a single particle, after subtraction of
the dissolved signal intensity, is proportional to the number of atoms in the particle which can be
converted to element mass and thus diameter to the third power, assuming a spherical particle
shape. The number of pulses counted is proportional to the nanoparticle number concentration.
The intensity of the continuum signal provides a measure of the dissolved metal content. The full
width (at 10 % peak height) of the transient signal from a single particle produced in an ICP-MS
has been measured to be on the order of 0.34 ms [3]. When using dwell times that are
significantly longer than the transient signal from a single particle, it is important that only one
particle is detected per measurement period; coincident particles would result in a bias. Particle
coincidence can be minimized by proper selection of the dwell time and by dilution of the
sample. If a particle event is split between adjacent measurement periods, the intensities in each
measurement period must be summed.
Samples are introduced into the ICP-MS as an aqueous suspension. Only a small
percentage of the sample solution is transported into the plasma. The ratio of the amount of
sample entering the plasma to the amount of sample introduced into the instrument is called the
transport efficiency. Three calibration strategies are currently employed to quantify particle size
and number concentration by spICP-MS: 1) Calibration of the instrument response using
reference nanoparticle standards spanning the linear mass/size range of interest [4]. 2)
Calibration of the instrument response using micro droplet generation [5], and 3) Measurement
of the transport efficiency followed by calibration of the instrument response with ionic standard
solution calibrants [6]. The last calibration strategy in this list is employed in this protocol.
Calibration of the ionic mass fraction concentration is accomplished by measuring ionic standard
solution calibrants.
Detection limits will depend on the elemental composition, the dissolved analyte content,
and the sensitivity of the particular commercial instrument being used. For chemically
homogenous NPs composed of a monoisotopic element (i.e., Au) and containing low mass
2
concentration of ions, diameters in the size range of 10 nm to 200 nm can be measured and
counted, but operating conditions may need to be adjusted to achieve a dynamic size range that is
linear [7].
3. Terminology
Analysis time (t): Total measurement time per sample, e.g. 60 s to 6 min
Dwell time (tdwell): The period during which the detector collects and integrates the
analytical signal (measurement window), e.g. 0.05 ms to 10 ms
Inductively Coupled Plasma Mass Spectrometry (ICP-MS): analytical technique used to
measure the elemental and/or isotopic composition of a sample, based on an instrument
comprising a sample introduction system, an inductively coupled plasma source for
generation of ions of the material(s) under investigation, a plasma/vacuum interface, and a
mass spectrometer comprising an ion focusing, separation and detection system [8].
Matrix: The majority component of a solution.
Nanoparticle: nano-object with all three external dimensions in the nanoscale [9].
Nanoparticle flux (fNP): The number of nanoparticles entering the plasma per unit of time,
e.g., s-1
Nanoparticle number concentration (NP): The number of nanoparticles per volume or mass
of solution, e.g., mL-1
, L-1
, g-1
, kg-1
Transport Efficiency (ηn): ratio of the number of particles or the mass of sample solution
entering the plasma to the number of particles or mass of sample solution introduced into
the instrument
Sample solution flow rate (qliq): The mass or volume of sample solution introduced into the
instrument per unit of time, e.g., g∙min-1
, mL∙min-1
4. Reagents, Materials, and Equipment
4.1 Reagents
4.1.1 De-ionized (DI) water (≥ 18 MΩ·cm resistivity)
Note: To achieve ultra-high purity (UHP) water, the DI feedstock water is
subjected to subboiling distillation in-house.
4.1.2 UHP Nitric Acid, HNO3 (Optima Grade, Fisher Scientific, Pittsburg, PA)
4.1.3 UHP Hydrochloric Acid, HCl (Optima Grade, Fisher Scientific, Pittsburg,
PA)
4.1.4 Thiourea (crystalline, ACS grade, 99 %, Alfa Aesar, Ward Hill, MA)
4.2 Materials
3
4.2.1 Reference Material (RM) 8011 Gold Nanoparticles, Nominal 10 nm Diameter
(NIST, Gaithersburg, MD)
4.2.2 RM 8012 Gold Nanoparticles, Nominal 30 nm Diameter (NIST,
Gaithersburg, MD)
4.2.3 RM 8013 Gold Nanoparticles, Nominal 60 nm Diameter (NIST,
Gaithersburg, MD)
4.2.4 Standard Reference Material (SRM) 3121 Gold (Au) Standard Solution
(NIST, Gaithersburg, MD)
4.2.5 SRM 3151 Silver (Ag) Standard Solution (NIST, Gaithersburg, MD)
4.2.6 RM 8017 PVP-Coated Silver Nanoparticles – Nominal Diameter 75 nm
(NIST, Gaithersburg, MD)
4.3 Labware
4.3.1 Fluorinated Ethylene-Propylene (FEP) or perfluoroalkoxy (PFA) Teflon 1-L
bottles
4.3.2 Nalgene low density polyethylene (LDPE) (30, 60, and 125) mL bottles
4.3.3 Falcon polypropylene 15 mL and 50 mL centrifuge tubes
4.3.4 High density polyethylene (HDPE) 4 mL scintillation vials
4.4 Equipment
4.4.1 ICP-MS capable of tdwell ≤ 10 ms
4.4.2 Analytical balance with readability of 0.1 mg
4.4.3 Ultrasonic bath
5. Reagent Preparation
5.1 Thiourea Diluent for Au standard solution
To improve the chemical stability, stability of the ICP-MS signal profile, and
wash out characteristics of dilute solutions of ionic Au, a diluent composed of 0.5
% mass fraction thiourea, 2.4 % volume fraction HCl, and 0.04 % volume fraction
HNO3 is used. Volume fraction is defined here as the volume of the constituent
divided by the total volume of the solution. The response factor for ionic Au was
tested in the thiourea diluent vs. water and found to be less than 5 % different.
5.1.1 Add 5.00 g of crystalline thiourea to a 1-L, tared, clean PFA or FEP Teflon
bottle followed by 500 g of UHP water. Cap and mix to dissolve the thiourea.
5.1.2 Add 24.00 mL (28.32 g) UHP HCl. Cap and mix.
5.1.3 Add 0.40 mL (0.56 g) UHP HNO3.
5.1.4 Dilute to a final volume of 1.00 L (998.20 g) with UHP water. Cap and mix.
5.2 Dilute HNO3 solution (2 % volume fraction)
Dilute HNO3 solution is used as a rinse between samples during ICP-MS analysis
and in the preparation of dilute ionic silver standard solutions. Improvement in
the chemical stability, stability of the ICP-MS signal profile, and wash out
characteristics for Ag were obtained in dilute acid relative to water alone. On
average, the response factor for ionic Ag in 2 % volume fraction HNO3 solution
was 10 % higher than the response factor for ionic Ag in water though it is
difficult to determine if the observed difference is due to a matrix effect in the
ICP-MS or loss of Ag.
4
5.2.1 Add 40 mL (56.00 g) UHP HNO3 to 1 L UHP water and dilute to 2 L
(1996.40 g) with UHP water.
6. Preparation of Ionic Standard Solution Calibrants
Ionic standard solution calibrants are needed to calibrate the response of the instrument.
The mass fractions given in Tables 1 and 2 serve as a guide and should be adjusted
depending on the sensitivity of the instrument. Mass fractions with resulting count rates
that span the range from 1.0E05 counts per second (cps) to 9.5 E05 cps are
recommended. A balance with a readability of 0.00001 g is used to record the masses for
each of the dilution steps.
6.1 Ionic Au Standard Solution Calibrants
Au standard solution calibrants prepared in thiourea diluent are stable for 1
month.
6.1.1 Au Stock Solution, Dilution 1 (Au Dil1), nominal 1.00E+05 ng/g Au
6.1.1.1 Record the mass of a clean, dry 60 mL LDPE bottle, AuB1
6.1.1.2 Add 0.5 g of SRM 3121 Gold (Au) Standard Solution to the bottle and
record the mass of the bottle + SRM 3121, AuS1.
6.1.1.3 Dilute to 50 g with thiourea diluent and record the mass of the bottle +
SRM 3121 + thiourea diluent, AuD1
6.1.1.4 Calculate the exact mass fraction of ionic Au in Dilution 1:
µg/g 𝐴𝑢 𝐷𝑖𝑙1 =
𝑚𝑔𝑔 𝑆𝑅𝑀 3121 × (𝐴𝑢𝑆1 − 𝐴𝑢𝐵1) × 1,000
𝐴𝑢𝐷1 − 𝐴𝑢𝐵1
6.1.2 Au Stock Solution, Dilution 2 (Au Dil2), nominal 1,000 ng/g Au
6.1.2.1 Record the mass of a clean, dry 60 mL LDPE bottle, AuB2
6.1.2.2 Add 0.5 g of Dilution 1 to the bottle and record the mass of the bottle +
Dilution 1, AuS2
6.1.2.3 Dilute to 50 g with thiourea diluent and record the mass of the bottle +
Dilution 1 + thiourea diluent, AuD2
6.1.2.4 Calculate the exact mass fraction of ionic Au in Dilution 2:
ng/g 𝐴𝑢 𝐷𝑖𝑙2 = µg/g 𝐴𝑢 𝐷𝑖𝑙1 × (𝐴𝑢𝑆2 − 𝐴𝑢𝐵2) × 1,000
𝐴𝑢𝐷2 − 𝐴𝑢𝐵2
6.1.3 Working Au Standards, nominal 5 ng/g Au, 15 ng/g Au, 30 ng/g Au
6.1.3.1 In the same manner as described above, prepare working Au standards
from Au Dil2 according to the Table 1. Three working standards are
minimum; additional standards can be prepared.
5
Table 1. Preparation of Working Au Standards
Nominal mass (g) of Au
Dil2
Nominal mass (g) of Au
Dil2 + thiourea diluent
Nominal mass fraction
(ng/g) Au Dil3
0.25 50 5
0.75 50 15
1.50 50 30
6.2 Ionic Silver (Ag) Standard Solution Calibrants
To improve the stability of dilute solutions of ionic Ag and improve signal
stability in the ICP-MS, Ag standards solutions are prepared in 2 % volume
fraction HNO3.
6.2.1 Ag Stock Solution, Dilution 1, nominal 1.00E+05 ng/g Ag
6.2.1.1 Using SRM 3151 Silver (Ag) Standard Solution, prepare in same manner
as described in 6.1.1, except use 2 % volume fraction HNO3 in place of
the thiourea diluent.
6.2.2 Ag Stock Solution, Dilution 2, nominal 1,000 ng/g Ag
6.2.2.1 Using Ag stock solution, Dilution 1, prepare in same manner as described
in 6.1.2, except use 2 % volume fraction HNO3 in place of the thiourea
diluent.
6.2.3 Working Ag Standards, nominal 2 ng/g Ag, 5 ng/g Ag, 8 ng/g Au
6.2.3.1 In the same manner as described above, prepare working Ag standards
from Ag Dil2 according to the Table 2. Three working standards are
minimum; additional standards can be prepared.
Table 2. Preparation of Working Ag Standards
Nominal mass (g) of
Ag Dil2
Nominal mass (g) of Au
Dil2 + 2 % volume
fraction HNO3 diluent
Nominal mass fraction
(ng/g) Ag Dil3
0.12 60 2
0.30 60 5
0.48 60 8
7. Sample Preparation
Proper dilution of the NP suspension prior to spICP-MS analysis is important. The intent
is to avoid, on one hand, the bias associated with more than one particle event occurring
per tdwell while at the same time maximizing the number of measured events occurring
during the total acquisition time, t. The first step is to calculate the target particle flux.
7.1 Determination of Target Particle Flux for spICP-MS Analysis
Laborda et al. suggest that the number of nanoparticles entering the ICP per unit of time,
i.e., the particle flux, fNP be calculated at the point where the systematic error in the
number of counted events arising from counting a 2-nanoparticle event as a single
nanoparticle event is approximately equal to the random error of the measurement
(derived by Poisson statistics from the total number of counted nanoparticle events) [10].
From [10], the systematic error, biasNP due to 2-nanoparticle events which are counted as
one nanoparticle can be expressed as:
6
biasNP ≈ 𝑡𝑑𝑤𝑒𝑙𝑙
2× 𝑓𝑁𝑃 (1)
The relative standard deviation (RSD) of the measurement, RSDNP is governed by
Poisson statistics and is derived from the analysis time, t and particle flux, fNP as follows:
RSDNP = 1
√𝑡 × 𝑓𝑁𝑃 (2)
The particle flux at which both error sources are equal can be derived by setting
equation 1 equal to equation 2, and solving for fNP as follows:
fNP = √4
𝑡 × 𝑡𝑑𝑤𝑒𝑙𝑙2
3 (3)
Thus, the target particle flux will depend on the chosen dwell and analysis times.
Equation 3 implies that for a given analysis time, t, smaller tdwell result in a higher
permissible particle flux with resulting better RSDNP. Table 3 shows the calculated fNP (s-
1) and RSDNP for an analysis time of 60 s and dwell times ranging from 1 ms to 10 ms.
Table 3. Calculated particle flux, fNP (s-1
) and theoretical measurement precision,
RSDNP for analysis time, t of 60 s and dwell times, tdwell ranging from 0.01
ms to 10 ms
tdwell (ms) fNP (s-1
) RSDNP
10 9 0.044
5 14 0.035
3 20 0.029
1 41 0.020
0.1 188 0.0094
0.05 299 0.0075
0.01 874 0.0041
However, there is a practical limit to be considered here. As the dwell time decreases the
likelihood that the nanoparticle event is split over adjacent measurement windows
increases. Liu et al. found that for data collected at a dwell time of 1 ms, over 40 % of
the particle events were spilt between adjacent measurement windows, and accurate
analysis required reconstruction of the NP event through additional data manipulation [7].
Currently, only a few commercially available ICP-MS systems provide software to count
and size NP events that are split over adjacent measurement windows. In light of these
competing considerations and when specialized software is not used, our protocol is to
use a dwell time of 10 ms, where the probability of a split event is reduced to 4 %, and to
improve the precision of the measurement by using longer analysis times. Table 4 shows
the calculated fNP (s-1
) and RSDNP for a dwell time of 10 ms and analysis times ranging
from 60 s to 360 s.
7
Table 4. Calculated particle flux, fNP (sec-1
) and theoretical measurement
precision, RSDNP for dwell time, tdwell of 10 ms and analysis times, t
ranging from 60 s to 360 s
t (s) fNP (s-1
) RSDNP
60 9 0.044
120 7 0.035
240 6 0.028
360 5 0.024
The values listed in Table 4 are used as an upper bound on the target particle flux.
7.2 Calculation of the Particle Number Concentration, NNP from the Target Particle
Flux
Once the target particle flux is determined, the particle number concentration (NNP) of the
diluted sample that will yield the desired flux can be calculated from the transport
efficiency (ηn) and the sample solution flow rate (qliq). Since calculation of the target
particle number concentration requires prior knowledge of the transport efficiency, and
determination of the transport efficiency requires measurement of a properly diluted
nanoparticle suspension, this will be an iterative process.
The target particle number concentration can be calculated as follows:
𝑁𝑁𝑃 = 𝑓𝑁𝑃 × 60
𝑞𝑙𝑖𝑞 × η𝑛
100⁄
where NNP is the target particle number concentration (g-1
), fNP is the target particle flux
(s-1
), qliq is the sample solution flow rate (g∙min-1
), and ηn is the transport efficiency
expressed as a percentage. Table 5 shows the calculated particle number concentration
for different particle flux, sample solution flow rates and transport efficiencies.
Table 5. Calculated particle number concentration, NNP for varying particle flux,
fNP , sample solution flow rate, qliq, and transport efficiency, ηn
fNP (s-1
) qliq (g∙min-1
) % ηn NNp (g-1
)
5 1 4 7,500
9 1 4 13,500
5 1 2 15,000
9 1 2 27,000
5 0.2 4 37,500
9 0.2 4 67,500
5 0.2 2 75,000
9 0.2 2 135,000
7.3 Calculation of the Particle Number Concentration From Known Mass
Concentration and Particle Size
8
Often, little is known about the particle number concentration of a sample suspension.
However, with knowledge of the total mass concentration (assuming all analyte present is
in nanoparticle form) and the expected particle size of the sample, the particle number
concentration can be calculated as follows:
𝑁𝑁𝑃 = 6 × 𝐶𝑆
1𝐸−15 × 𝑑𝑝3 × 𝜋 × 𝜌
where NNP is the target particle number concentration (g-1
), CS is the mass fraction of the
analyte in the sample (µg∙g-1
), dp is the diameter of the particle (nm), π is pi and ρ is the
density of the particle (g∙cm-3
). Table 6 lists the calculated particle number concentration
for NIST nanoparticle RMs value assigned for mass fraction and nanoparticle size. For
consistency, the particle size measured by transmission electron microscopy (TEM) is
used.
Table 6. Calculated particle number concentration, NNP for NIST nanoparticle
RMs value assigned for mass fraction and nanoparticle size
RM 8011 8012 8013 8017
Composition Au Au Au Ag
densitya 19.3 19.3 19.3 10.49
CS (µg∙g-1
) 51.56 48.17 51.86 1,081b
TEM diameter (nm) 8.9 27.6 56 74.6
Calculated NNP (g-1
)c 7.237E+12 2.267E+11 2.922E+10 4.741E+11
aof bulk metal;
bassumes reconstitution with 2.000 g water,
cbased on assumption that all
analyte is present as spherical nanoparticles of the listed TEM – measured diameter.
7.4 Preparation of Working Nanoparticle Suspensions of NIST RMs
NIST RMs must be serially diluted to obtain working suspensions with particle number
concentrations suitable for spICP-MS analysis. Table 7 shows a possible dilution
scheme for RMs 8011, 8012, 8013, and 8017 to achieve a particle number concentration
of 3.0E+04 g-1
. In general, high purity water is used as the diluent in the preparation of
these suspensions, but for reactive elements such as Ag, care must be exercised and
alternative diluents may be useful for stabilizing the suspension. Clean, dry, 60 mL and
125 mL LDPE bottles or 50 mL polypropylene centrifuge tubes are used as preparation
vessels. A balance with a readability of 0.00001 g is used to record the masses for each
of the dilutions steps. When preparing NP suspensions, it is advisable to add the diluent
to the bottle first followed by the aliquot of the suspension being diluted. Pipet tips
should be conditioned with the suspension prior to aliquoting. Each diluted suspension
is sonicated for one minute in an ultrasonic bath. Nominal mass fractions (CS) of each
dilution are listed in Table 7.
Table 7. Preparation of Working Nanoparticle Suspensions of NIST RMs
RM 8011 8012 8013 8017
Dilution 1a, b
mass (g) of RM 0.200 0.250 0.500 0.200
mass (g) RM + water 125 50.0 50.0 50.0
9
CS Dil1 (ng/g) 82.5 241 519 4324
NNP Dil1 (g-1
) 1.16E+10 1.13E+09 2.92E+08 1.90E+09
Dilution 2
mass (g) of Dil1 0.200 0.250 0.500 0.200
mass (g) Dil1 + water 125 50.0 50.0 50.0
CS Dil2 (ng/g) 0.132 1.20 5.19 17.30
NNP Dil2 (g-1
) 1.85E+07 5.67E+06 2.92E+06 7.58E+06
Dilution 3
mass (g) of Dil2 0.203 0.265 0.514 0.198
mass (g) Dil2 + water 125 50.0 50.0 50.0
CS Dil3 (ng/g) 0.000214 0.00638 0.0533 0.0685
NNP Dil3 (g-1
) 3.01E+04 3.00E+04 3.00E+04 3.00E+04 aNote 1: For RMs 8011 – 8012: Thoroughly mix the vial by inverting several times, do
not sonicate the starting material. Inspect for proper appearance. Dilute suspensions of
AuNPs should be prepared daily.
bNote 2: For RM 8017: Reconstitute RM 8017 per the instructions on the Report of
Investigation (ROI) using 2.000 g water. Do not sonicate the reconstituted suspension.
Data on the stability of reconstituted RM 8017 stored at 4 °C shows minimal
degradation of the Ag nanoparticles over a period of 90 d, but dilute suspensions of
AgNPs prepared in water are unstable. Dilutions should be performed the day of
analysis, and the working suspension should be analyzed within one half hour of
preparation if water is used as the diluent.
8. ICP-MS Analysis
Any ICP-MS system that can be operated in time-resolved analysis mode (TRA) and is
capable of tdwell ≤ 10 ms can be used for spICP-MS analysis. A ThermoFisher X series 2
quadrupole ICP-MS system was used to collect the data reported in this protocol. The
plasma is operated at a forward power of 1400 W, and the plasma and auxiliary flows are
set to 14 L∙min-1
and 0.9 L∙min-1
, respectively. The nebulizer flow is adjusted daily to
achieve optimum conditions, but is typically between 0.8 L∙min-1
and 0.9 L∙min-1
. Sample
solutions are introduced into the ICP via a peristaltic pump and a micro-flow
perfluoroalkoxy (PFA) concentric nebulizer (PFA-ST, Elemental Scientific, Omaha, NE,
USA) attached to an impact bead spray chamber cooled to 2 °C. The sample solution
flow rate (qliq), nominally 0.2 g∙min-1
, is measured daily in triplicate. The transport
efficiency, which will vary with the sample introduction system (i.e., type of nebulizer
and spray chamber), operating conditions, (i.e., gas flows and cone type), and sample
matrix, is measured daily using both the particle frequency method and the particle size
method reported in Pace et al. [6]
8.1 Optimization of operating conditions
Operating conditions are optimized per manufacturer recommendations. A tune
solution containing lithium (Li), indium (In), cerium (Ce) and uranium (U) is
used; nebulizer gas flow and lens settings are adjusted to obtain maximum
sensitivity for 115
In and then further adjusted until an acceptable 156
CeO+/140
Ce+
ratio is obtained. Gold and Ag are intentionally absent from the tune solution in
order to keep the instrument background low for those elements. ThermoFisher X
10
series ICP-MS instruments are supplied with two skimmer cone types, the matrix
tolerant Xt skimmer cone, and the higher sensitivity, Xs cone. The Xs cone
provides the best detection limits; ≥ 700 cps can be obtained for 10 nm AuNPs,
but at the expense of the 156
CeO+/140
Ce+ ratio, which is typically 6 % to 15 % for
the chosen tune conditions. Due to the greater sensitivity for the Xs cones, the
upper size range is limited to about 60 nm AuNPs. Particles larger than this may
exceed the linear dynamic range of the pulse counting detector since the signal
intensity for a spherical particle scales by a power of three relative to the particle
diameter. Though a linear relationship between the pulse stage and analog stage
of the detector can be achieved for ionic standards, our experience with
particulate suspensions is that non- linearity is observed for suspensions
containing large particles whose signal intensity exceeds the range of the pulse
detector. Reducing sensitivity will extend the measureable size range. The Xt
cones are used for routine analysis; conditions are chosen so the 156
CeO+/140
Ce+
ratio is < 2 %, and AuNPs in the range of 20 nm to 80 nm can be measured. The
upper measurable size range can be extended by lowering the signal intensity
using collision cell/kinetic energy discrimination mode or by lowering the
extraction voltage [7]. As the Ag isotopes are half as abundant as the Au isotope,
the lower size limit is 20 nm for AgNPs using the Xs cones, and the upper limit is
100 nm AgNPs with Xt cones under standard conditions. Different ICP-MS
systems will have different lower and upper size detection limits depending on the
sensitivity of the system.
8.2 Analysis Parameters
8.2.1 Au: The 197
Au intensity is recorded in TRA mode using a dwell time of 10 ms
for total analysis times (t) ranging from 100 s to 360 s.
8.2.2 Ag: The 107
Ag intensity is recorded in TRA mode using a dwell time of 10 ms
for total analysis times (t) ranging from 100 s to 360 s.
8.3 Measurement of the Transport Efficiency
Measurement of the transport efficiency via the methods outlined in Pace et al.,
the particle frequency method and the particle size method, requires measurement
of the sample flow, analysis of ionic standards (size method), and analysis of a
standard nanoparticle suspension of known size and mass concentration or
particle number concentration [6] . Calibration of the transport efficiency in this
way means that the overall uncertainty of the spICP-MS measurement of size and
number concentration is directly related to the measurement method and its
associated uncertainty used to value assign the standard nanoparticle suspension.
We use RM 8013 and the size value assigned by TEM, 56 nm ± 0.5 nm. The
derived particle number concentration for RM 8013 is shown in Table 6, and
preparation of the working suspension is described in section 7.4.
Pace et al. reports similar values for the transport efficiency measured using
either the frequency or size method, but we have at times observed that the
transport efficiency measured via the particle frequency method is lower than that
measured by the particle size method. Loss of NPs to the container walls and
pump tubing from the very dilute suspensions required for spICP-MS would
result in a low bias in the transport efficiency measured via the particle frequency
method and could possibly explain at least some of the differences we observe.
11
Tuoriniemi et al. have also identified analyte partitioning effects during
nebulization and off axis trajectories of particles in the plasma as other
considerations that may affect the accurate measurement of the transport
efficiency [11]. Our protocol is to measure the transport efficiency using both
methods (described below), however, our experience has been that when a
difference is observed, the particle size method yields more accurate results.
8.3.1 Measurement and Calculation of sample flow rate, qliq
The sample flow is the amount of sample solution entering the instrument
per unit of time.
8.3.1.1 Measure the total starting mass of the sample solution and its container
using a balance with a readability of 0.0001 g. Record as mstart (g)
8.3.1.2 Using a stop watch, measure the time from when the sample solution
uptake starts to the point where the probe leaves the solution. Record as
tuptake (min)
8.3.1.3 Measure and record the mass of the remaining sample solution and its
container mend (g)
8.3.1.4 Calculate the sample solution flow rate (qliq) as:
sample solution flow rate (𝑔 ∙ 𝑚𝑖𝑛−1) = 𝑚𝑒𝑛𝑑 − 𝑚𝑠𝑡𝑎𝑟𝑡
𝑡𝑢𝑝𝑡𝑎𝑘𝑒
8.3.2 Analysis sequence for the measurement of the transport efficiency
8.3.2.1 Aspirate thiourea solution until instrument background at m/z 197 is at
lowest achievable level.
8.3.2.2 Run samples in the following run sequence: thiourea diluent, water, NP
reference material (i.e., RM 8013 – D-3, see Table 7), working Au
standards from low to high concentration. If desired a second NP reference
material (i.e., RM 8012 – Dil3) can be run and used as an accuracy check.
At least three replicates of the NP reference material are measured and the
results averaged.
8.3.3 Data Analysis
8.3.3.1 Using a spread sheet program such as Microsoft Excel, multiply the data
recorded in counts per second by the dwell time, tdwell, in order to convert
to counts per measurement window.
8.3.3.2 Distinguishing particle events from background
Particle events are distinguished from the background using a n times
standard deviation (n × σ) criterion as described below. Tuoriniemi et al.
suggest that in order to reduce the number of false positives (signals
counted as a particle, but which are not particles) to less than 0.1 % of the
total count, n values larger than 3 must be used. They recommend a value
of n = 5 as a compromise between minimization of the number of false
positives, while not omitting too many particles from being counted that
are in fact particles.
8.3.3.2.1 Order the count data for each sample from largest to smallest
8.3.3.2.2 Compute the mean (µ), standard deviation (σ), and µ + 5 × σ
12
8.3.3.2.3 Using the value for µ + 5 × σ as the cutoff between particle signal
and background, remove the particle signals from the population
and move these data points to a different ‘particle events’ column.
8.3.3.2.4 Compute the mean (µ), standard deviation (σ), and µ + 5 × σ of the
remaining population of data points. If additional particle signals
exceed the new value for µ + 5 × σ, again remove the particle
signals from the population and move these data points to the
‘particle events’ column. Continue this iterative process until none
of the remaining data points exceeds µ + 5 × σ.
8.3.3.2.5 Compute the mean of the data points not considered particle
events, this is the intensity of the dissolved or ionic fraction, Idiss.
Note that this population may also include particles that are too
small to be detected as particles.
8.3.3.2.5.1 Correct Idiss for instrument background by subtracting the mean
of the population of data points measured for the water sample.
8.3.3.3 Split Particle Correction
The transport of particles into the plasma is a random process. It is
possible that a particle event may occur near the end of one measurement
period (dwell time) and spill over into the start of the adjacent
measurement period. This is considered a split particle event. As discussed
in section 7.1, when the chosen dwell time approaches the width of a
single particle event, the likelihood that a particle event is spilt between
adjacent measurement windows increases. For samples of known
monodispersity, as should be the case for the NP standard being used to
measure the transport efficiency, it is possible to correct for split particle
events. Examples of split particle correction for various tdwell are given in
a spreadsheet in the Supporting Information of [7] and will not be
described in detail here. Briefly, the temporal data are examined to locate
occurrences where signal was observed in adjacent measurement
windows. The intensity of the signal in each adjacent measurement
window is compared to the intensity that would be expected for a single
particle event contained completely within one dwell time. If either or
both of the observed intensities in the adjacent measurement windows are
more than 25 % lower than the expected intensity, then the signals are
assumed to be from a single particle event and this split particle event is
corrected by summing the two intensities.
8.3.3.4 Visual inspection for false positives
A false positive is a signal counted as a particle, but which is not a
particle. Though the n times standard deviation (n × σ) criterion described
above is selected to reduce the number of false positives, some false
positives remain in the data set. In situations where the measured
suspension is believed to be monodisperse, contains particles well above
the size detection limit, and contains little or no dissolved analyte, the data
13
set can be visually examined for false positives. In this case, a large gap
(greater than a factor of ten) will exist between the intensity of a true
particle event and false positive events.
8.3.3.5 Compute the mean of the data points considered particle events corrected
for split particle events and false positives. This is the intensity of the
particle events, INP.
8.3.3.5.1.1 Correct INP for the dissolved background by subtracting Idiss
(see 8.3.3.2.5).
8.3.3.6 Count the number of data points considered particle events corrected for
split particle events and false positives (CountNP)
8.3.3.7 Compute the nanoparticle flux, fNP (s-1
)
𝑓𝑁𝑃 (𝑠−1) =𝐶𝑜𝑢𝑛𝑡𝑁𝑃
𝑡𝑎𝑛𝑎𝑙𝑦𝑠𝑖𝑠
where CountNP is the number of particle events measured (see 8.3.3.6)
during the analysis time (t, sec, see 8.2.1).
8.3.4 Calculation of Transport Efficiency via the Particle Frequency Method, ηnPF
η𝑛𝑃𝐹 =𝑓𝑁𝑃
𝑁𝑁𝑃 𝑅𝑀 𝐷𝑖𝑙3 × 𝑞𝑙𝑖𝑞
60⁄
where fNP (s-1
) is the nanoparticle flux measured for the nanoparticle reference
material, NNp RM Dil3 (g-1
, Table 7) is the calculated particle number
concentration of the gravimetrically diluted nanoparticle reference material,
and qliq is the sample flow (g∙min-1
)
8.3.5 Calculation of Transport Efficiency via the Particle Size Method, ηnPS
8.3.5.1 Construct mass per measurement period (tdwell) calibration curve for ionic
standards to derive the ionic response factor, RFionic
8.3.5.1.1 Compute mean measured counts for working Au standards, IAu ionic,
and correct for instrument background by subtracting the mean of
the population of data points measured for the thiourea diluent.
8.3.5.1.2 Compute the mass of dissolved Au standard (ng) introduced into
the instrument per measurement period, massAu ionic, from the mass
concentrations of working standards (Table1):
𝑚𝑎𝑠𝑠𝐴𝑢 𝑖𝑜𝑛𝑖𝑐 (𝑛𝑔) =𝐴𝑢 𝐷𝑖𝑙3 × 𝑞𝑙𝑖𝑞 × 𝑡𝑑𝑤𝑒𝑙𝑙
6.0E+04
14
where Au Dil3 is the mass fraction of ionic Au in the working
standards (nominal 5 ng/g to 30 ng/g Au), qliq is the sample flow
(g∙min-1
), tdwell is the dwell time (ms).
8.3.5.1.3 Plot IAu ionic vs. massAu ionic for each Au working standard and using
the regression function of Microsoft Excel, compute the slope with
units of counts∙ng-1
, this is the ionic response factor, RFionic. The
regression function of Microsoft Excel also computes the standard
error of the slope which can be used in the computation of the
standard uncertainty of the transport efficiency measurement (see
Uncertainty section).
8.3.5.2 Compute response factor (RFNP) for NP standard
8.3.5.2.1 Compute the mass of the NP in the NP standard, massNP RM (ng)
𝑚𝑎𝑠𝑠𝑁𝑃 𝑅𝑀(𝑛𝑔) = 𝑑𝑝 𝑅𝑀 3 × 𝜋 × 𝜌 × 1E−12
6
where dp RM is the diameter of the particle (nm) in the standard, π is
pi and ρ is the density of the particle (g∙cm-1
). For use of RM 8013
as the NP standard, the particle size measured by TEM, 56 nm, is
used (see section 8.3), and the calculated massNP RM is 1.775 E-
06 ng Au.
8.3.5.2.2 Compute the response factor of the NP standard, RFNP RM
𝑅𝐹𝑁𝑃 𝑅𝑀 =𝐼NP RM − 𝐼diss RM
𝑚𝑎𝑠𝑠NP RM
where INP RM is the intensity of the particle events, Idiss RM is the
intensity of the dissolved background (counts, see 8.3.3.5) and
massNP RM is the mass Au in a single NP within the NP standard
(ng, see 8.3.5.2.1).
8.3.5.3 Compute the Transport Efficiency (particle size method), ηnPS
𝜂𝑛𝑃𝑆 =𝑅𝐹𝐴𝑢 𝑖𝑜𝑛𝑖𝑐
𝑅𝐹𝑁𝑃 𝑅𝑀
where RFAu ionic is the slope of the calibration curve formed by a plot of IAu
ionic vs. massAu ionic for each Au working standard (counts∙ng-1
, see
8.3.5.1.3) and RFNP is the response factor of the NP standard (counts∙ng-1
,
see 8.3.5.2).
8.4 Measurement of ‘Unknown’ Ag Nanoparticle Suspension
8.4.1 Dilute samples to target particle number concentration (See section 7)
Note: Dilution of unknowns to the target particle number concentration requires a priori
knowledge of the particle size and mass concentration of the NPs in the suspension. If this
15
information is not available, a series of dilutions must be analyzed to demonstrate the
absence of particle coincidence.
8.4.2 Aspirate 2 % volume fraction nitric acid solution until instrument background
at m/z 107 is at lowest achievable level.
8.4.3 Run samples in the following run sequence: 2 % volume fraction nitric acid
solution, water, unknowns from low NNP to high NNP, working Ag standards
from low to high concentration.
Note: Dilute suspensions of AgNPs are reactive and should be prepared within
30 min of analysis or prepared in a diluent that will stabilize the AgNPs.
8.4.4 Perform data analysis as described in section 8.3.3.
Note: Split particle correction and visual inspection for false positives may not
be possible for the analysis of unknown suspensions.
9. Calculation of Particle Number Concentration of ‘Unknown ‘ Suspension of AgNPs
𝑁𝑁𝑃 𝑢𝑛𝑘𝑛𝑜𝑤𝑛 = 𝐶𝑜𝑢𝑛𝑡𝑁𝑃 𝑢𝑛𝑘𝑛𝑜𝑤𝑛
𝑡𝑎𝑛𝑎𝑙𝑦𝑠𝑖𝑠 × 𝑞𝑙𝑖𝑞
60⁄ × ηn × 𝐷𝑖𝑙𝑢𝑡𝑖𝑜𝑛 𝐹𝑎𝑐𝑡𝑜𝑟
where CountNPunknown is the number of particle events measured during the
analysis time, tanalysis (s), qliq is the sample flow (g∙min-1
), and ηn is the transport
efficiency (section 8.3). Logically the transport efficiency measured via the
particle frequency method, ηnPF, can be used, but only if there is no significant
difference between ηnPF and ηnPS.
10. Calculation of Particle Mass, Particle Diameter, and Particle Size Distribution of
‘Unknown’ Suspension of AgNPs
10.1 Construct mass per measurement period calibration curve for ionic standards
10.1.1 Compute mean measured counts for working Ag standards, IAg ionic, and
correct for instrument background by subtracting the mean of the population
of data points measured for the 2 % volume fraction nitric acid diluent.
10.1.2 Compute the mass of dissolved Ag standard (ng) introduced into the
instrument per measurement period, massAg ionic, from the mass concentrations
of working standards (Table 2):
𝑚𝑎𝑠𝑠𝐴𝑔 𝑖𝑜𝑛𝑖𝑐(𝑛𝑔) =𝐴𝑔 𝐷𝑖𝑙3 × 𝑞𝑙𝑖𝑞 × 𝑡𝑑𝑤𝑒𝑙𝑙
6.0E+04
where Ag Dil3 is the mass fraction of ionic Ag in the working standards
(nominal 2 ng/g to 8 ng/g Au), qliq is the sample flow (g∙min-1
), tdwell is the
dwell time (ms).
10.1.3 Plot IAg ionic vs. massAg ionic for each Ag working standard, and using the
regression function of Microsoft Excel, compute the slope with units of
counts∙ng-1
, which is RFAg ionic. The regression function also computes the
standard error of the slope which can be used in the computation of the
standard uncertainty of the mass or size measurement.
10.2 Compute the mass of the ‘unknown’ particle, massNP (ng)
16
𝑚𝑎𝑠𝑠𝑁𝑃 =((𝐼𝑁𝑃 − 𝐼𝑑𝑖𝑠𝑠) × ηn𝑃𝑆)
𝑅𝐹𝐴𝑔 𝑖𝑜𝑛𝑖𝑐
where INP is the intensity of the particle event, Idiss is the intensity of the
dissolved background (counts, see 8.3.3.5), ηnPS is the transport efficiency
measured via the particle size method, and RFAg ionic is the slope of the
calibration curve formed by a plot of IAg ionic vs. massAg ionic for each Ag
working standard (counts∙ng-1
, see 10.1.3). Compute the diameter of the
unknown’ particle, dp (nm)
𝑑𝑝 = √6 × 𝑚𝑎𝑠𝑠𝑁𝑃
𝜋 × 𝜌 × 1E−12
3
where massNP is the mass of the particle (ng, see 10.2), π is pi and ρ is the density
of the particle (g∙cm-1
).
10.3 Compute the particle size distribution
10.3.1 Compute the diameter of each particle event (sections 10.2 and 10.3).
10.3.2 Create a ‘bin’ column with 1 nm size increments spanning the observed
particle size range.
10.3.2.1 Using the data analysis tool of Microsoft Excel, choose the histogram
function. Choose the appropriate particle diameter and bin range data
columns, specify the output range, and select chart output.
11. Calculation of the Analyte Mass Fraction (ng∙g-1) in the ionic fraction, Conionic
𝐶𝑜𝑛𝑖𝑜𝑛𝑖𝑐 = 𝐼𝑑𝑖𝑠𝑠
𝑅𝐹𝑖𝑜𝑛𝑖𝑐 × 𝑞𝑙𝑖𝑞
60⁄ × 𝑡𝑑𝑤𝑒𝑙𝑙
1000⁄
where Idiss is the intensity of the dissolved or ionic fraction, corrected for instrument
background (see 8.3.3.2.5.1), RFionic is the slope of the calibration curve formed by a plot
of IAg ionic vs. massAg ionic for each Ag working standard (counts∙ng-1
, see 10.1.3), qliq is the
sample flow (g∙min-1
), and tdwell is the dwell time (ms).
12. Computation and Uncertainty Analysis via the Kragten Spreadsheet
To gain insight into the accuracy of spICP-MS measurements and to enable
comparison with established methods, the uncertainty of the measurement must be
quantified. For this purpose a Kragten spreadsheet is used, because it provides a simple
and practical approach to: 1. compute a result via the equations described above, 2.
combine the uncertainties associated with each component of the measurement equation
to derive an estimated expanded uncertainty, and 3. determine where the major sources of
uncertainty lie so that the measurement process can be improved [12, 13]. In Tables 8
through Table 11 below, example Kragten spreadsheets for the spICP-MS measurement
17
of transport efficiency via the size and frequency methods, particle number concentration,
and particle size are shown.
The displayed Kragten spreadsheets are color coded to draw the reader’s attention
to certain key areas of the spreadsheet. The first three columns highlighted in yellow
describe each component of the measurement equation, list the symbol, and show typical
input values. The lime green highlighted rows at the top of each spreadsheet show the
estimated standard uncertainty, ui, of each component appearing in column 2. A brief
description of how standard uncertainties were evaluated for each measurement equation
component appears in row 3. Uncertainty estimates are evaluated by Type A and Type B
methods. Degrees of freedom, i, for each component are shown in the fourth row,
highlighted in blue. The degrees of freedom for Type A evaluations are computed as n –
1 and Type B evaluations are estimated to have 60 degrees of freedom. The
measurement function (MF) value, or calculated result of the measurement equation, is
shown in the pink row appearing under the yellow-highlighted measurement component
columns. Finally, the first column of the bottom five rows of the Kragten spreadsheet
show the combined standard uncertainty (uc), the effective degrees of freedom (νeff), the
coverage factor (k), the expanded uncertainty (U) and the relative expanded uncertainty
expressed in percent (Ur).
The combined standard uncertainty is the square root of the sum of the squares
(RSS = √∑ (𝑐𝑖𝑢𝑖)2𝑛𝑖=1
2 ) of the individual uncertainty components, each scaled to reflect its
impact on the final result based on the measurement equation. The Kragten uses a
numeric approximation to the scaled RSS to combine uncertainty components. The
expanded uncertainty is calculated as U = kuc, where the value of k is determined from
the Student’s t distribution with eff effective degrees of freedom. An approximately 95
% confidence interval for the measured is obtained. The effective degrees of freedom are
calculated from the Welch-Satterthwaite formula (shown in [14], appendix B.3).
Adjacent to the effective degrees of freedom cell and highlighted in red font, the relative
contribution of each component, calculated as its variance relative to the total variance, is
shown. From this row, the reader can quickly discern which component or components
most influence the overall uncertainty of the measurement.
18
Table 8. Kragten Spreadsheet for Transport Efficiency via the Particle Frequency Method, ηnPF
u(C Au+) u(d RM8013 -TEM) u(aliquot RM) u(Dil. mass, Dil1) u(aliquot Dil1) u(Dil. mass, Dil2) u(aliquot Dil2) u(Dil. mass, Dil3) u(ρ Au) u(CountNP) u(qliq) u(tanalysis)
0.32 0.25 0.00017 0.00017 0.00017 0.00017 0.00017 0.00017 0.010 8.2 0.00091 0.024
Description
combined
standard
uncertainty of the
Au mass fraction
measurement for
RM 8013 AuNPs,
Nominal 60 nm
Diameter from the
ROI
combined standard
uncertainty of the TEM
particle size
measurement for RM
8013 AuNPs, Nominal
60 nm Diameter from
the ROI
estimated standard
uncertainty of the
mass measured on a
5-place analytical
balance from an
assumed rectangular
probability distribution
of magnitude
0.00030 g
see column 6 see column 6 see column 6 see column 6 see column 6
estimated standard
uncertainty for the
density of Au from an
assumed rectangular
probability distribution
of magnitude 0.018
based on variance of
values reported in the
literature.
standard
uncertainty of the
mean measured
number of nominal
60 nm AuNPs for
four replicate runs
of RM 8013
standard
uncertainty of
three replicate
measurements of
the sample flow
rate
standard
uncertainty of the
analysis time for
four replicate runs
of RM 8013
degrees of
freedom i60.00 60.00 60.00 60.00 60.00 60.00 60.00 60.00 60.00 3.0 2.0 3.0
Quantity DescriptionQuantity
Name, Quantity Value
mass fraction Au+ in NP
standard (µg∙g-1
)
C S Au+ RM
801351.86 52.18 51.86 51.86 51.86 51.86 51.86 51.86 51.86 51.86 51.86 51.86 51.86
diameter AuNP in NP
standard (nm) d RM8013 - TEM56.00 56.00 56.25 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00
mass of NP standard (g)mass RM
80130.04906 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
dilute to mass (=D-1) (g)Dil. mass,
Dil 131.14147 31.14 31.14 31.14 31.14 31.14 31.14 31.14 31.14 31.14 31.14 31.14 31.14
aliquot mass Dil1 (g) aliquot Dil 1 0.49120 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49 0.49
dilute to mass (=D-2) (g)Dil. mass,
Dil 230.95389 30.95 30.95 30.95 30.95 30.95 30.95 30.95 30.95 30.95 30.95 30.95 30.95
aliquot mass Dil2 (g) aliquot Dil 2 1.17502 1.18 1.18 1.18 1.18 1.18 1.18 1.18 1.18 1.18 1.18 1.18 1.18
dilute to Mass (=D-3) (g)Dil. mass,
Dil 361.72538 61.73 61.73 61.73 61.73 61.73 61.73 61.73 61.73 61.73 61.73 61.73 61.73
density of Au (g∙cm-1)ρ Au
19.30 19.30 19.30 19.30 19.30 19.30 19.30 19.30 19.30 19.31 19.30 19.30 19.30
measured number of
particlesCount NP 214.0 214.00 214.00 214.00 214.00 214.00 214.00 214.00 214.00 214.00 222.18 214.00 214.00
sample flow rate (g∙min-1) q liq0.17442 0.17442 0.17442 0.17442 0.17442 0.17442 0.17442 0.17442 0.17442 0.17442 0.17442 0.17533 0.17442
analysis time (sec) t analysis 179.74 179.74 179.74 179.74 179.74 179.74 179.74 179.74 179.74 179.74 179.74 179.74 179.76
MF Value, ηnPF0.0295
0.0293 0.0298 0.0293 0.0295 0.0294 0.0295 0.0294 0.0295 0.0295 0.0306 0.0293 0.0294
-1.81E-04 3.96E-04 -1.04E-04 1.64E-07 -1.04E-05 1.65E-07 -4.34E-06 8.26E-08 1.59E-05 1.13E-03 -1.52E-04 -3.98E-06 c i u i
Combined Standard Uncertainty, u c 0.00123.26E-08 1.57E-07 1.07E-08 2.68E-14 1.08E-10 2.72E-14 1.88E-11 6.83E-15 2.51E-10 1.27E-06 2.31E-08 1.59E-11 (c i u i )
2
Degrees of Freedom, 4.15
2.2% 10.5% 0.7% 0.000002% 0.01% 0.000002% 0.001% 0.0000005% 0.02% 85.0% 1.6% 0.001% rel (c i u i )2
Coverage Factor, k2.78
-5.64E-04 1.58E-03 -5.98E-01 9.46E-04 -5.99E-02 9.51E-04 -2.51E-02 4.77E-04 1.53E-03 1.38E-04 -1.68E-01 -1.64E-04 ci
Expanded Uncertainty, U0.0034
% Relative Expanded Uncertainty U r11.5%
Quantity Value + u i
Standard
Uncertainty, u i
19
Table 9. Kragten Spreadsheet for Transport Efficiency via the Particle Size Method, ηnPS
aThe estimated standard error (SE) of the dead time correction was evaluated by Type B methods to be of magnitude 5 % relative
based on a DT correction of 37 ns for NP signals measured using 0.1 ms tdwell.
u(RFAu ionic) u(d RM8013 -TEM) u(ρ Au) u(INP AuNP) u(Idiss Au)
43183.93 0.25 0.010 15.5 0.014
Description
standard error of the slope
of the plot of IAu ionic vs.
massAu ionic as computed
using the regression
function of Microsoft Excel
combined standard
uncertainty of the TEM
particle size measurement
for RM 8013 AuNPs,
Nominal 60 nm Diameter
from the ROI
estimated standard
uncertainty for the
density of Au from an
assumed rectangular
probability distribution of
magnitude 0.018 based
on variance of values
reported in the literature.
standard uncertainty of
the mean measured
intensity of nominal 60
nm AuNPs composed
of the SE of four
replicate runs of RM
8013 added in
quadrature to the
estimated SE for
deadtime correctiona
standard
uncertainty of the
mean measured
intensity of the
dissolved Au
background for four
replicate runs of RM
8013
degrees of
freedom i2.00 60.00 60.00 19.25 3.00
Quantity DescriptionQuantity
Name, SymbolQuantity Value
slope of the calibration
curve formed by a plot of RF Au ionic 8,709,175.69 8,752,359.62 8,709,175.69 8,709,175.69 8,709,175.69 8,709,175.69
diameter AuNP in NP
standard (nm)d RM8013 - TEM 56.00 56.00 56.25 56.00 56.00 56.00
density of Au (g∙cm-1) ρ Au 19.30 19.30 19.30 19.31 19.30 19.30
intensity of the particle
events (counts)I NP RM 8013 417.57 417.57 417.57 417.57 433.06 417.57
intensity of the dissolved
background (counts)I diss RM 8013 0.138 0.14 0.14 0.14 0.14 0.15
MF Value, ηnPS0.03703 0.03721 0.03752 0.03705 0.03570 0.03703
1.84E-04 4.98E-04 1.99E-05 -1.33E-03 1.28E-06 c i u i
Combined Standard Uncertainty, u c 0.00143 3.37E-08 2.48E-07 3.98E-10 1.76E-06 1.65E-12 (c i u i )2
Degrees of Freedom, 25.67 1.7% 12.2% 0.020% 86.2% 0.00008% rel (c i u i )2
Coverage Factor, k 2.06 4.25E-09 1.99E-03 1.92E-03 -8.55E-05 8.87E-05 ci
Expanded Uncertainty, U 0.0029
% Relative Expanded Uncertainty U r7.94%
Quantity Value + u i
Standard
Uncertainty, u i
20
Table 10. Kragten Spreadsheet for Determination of Particle Number Concentration of ‘Unknown’ AgNP Solution
u(ηnPS) u(CountNP) u(tanalysis) u(qliq) u(to mass, D-3) u(mass Dil2) u(to mass, D-2) u(mass Dil1) u(to mass, D-1) u(mass RM)
0.00143 27.36 0.01436 0.00091 0.00017 0.00017 0.00017 0.00017 0.00017 0.00017
Description
standard
uncertainty of the
measured transport
efficiency (particle
size method) from
Kragten
Spreadsheet
standard
uncertainty of the
mean measured
number of particles
for four individual
vials of "unknown"
RM 8017
standard
uncertainty of the
analysis time for
four analyses
standard
uncertainty of three
replicate
measurements of
the sample flow rate
Estimated standard
uncertainty of the
mass measured on
a 5-place analytical
balance from an
assumed
rectangular
probability
distribution of
magnitude
0.00030 g
see column 8 see column 8 see column 8 see column 8 see column 8
degrees of
freedom i4.15 3.00 3.00 2.00 60.00 60.00 60.00 60.00 60.00 60.00
Quantity DescriptionQuantity
Name, SymbolQuantity Value
transport efficiency (particle
size method)ηnPS 0.03703 0.03845 0.03703 0.03703 0.03703 0.03703 0.03703 0.03703 0.03703 0.03703 0.03703
measured number of
particlesCount NP 766.0 766.0 793.4 766.0 766.0 766.0 766.0 766.0 766.0 766.0 766.0
analysis time (sec) t analysis 359.84 359.84 359.84 359.85 359.84 359.84 359.84 359.84 359.84 359.84 359.84
sample flow rate (g∙min-1)q liq 0.17565 0.17565 0.17565 0.17565 0.17656 0.17565 0.17565 0.17565 0.17565 0.17565 0.17565
dilute to Mass (=D-3) (g) Dil. mass, Dil 3 58.41995 58.41995 58.41995 58.41995 58.41995 58.42012 58.41995 58.41995 58.41995 58.41995 58.41995
aliquot mass Dil2 (g) aliquot Dil 2 0.77753 0.77753 0.77753 0.77753 0.77753 0.77753 0.77770 0.77753 0.77753 0.77753 0.77753
dilute to mass (=D-2) (g) Dil. mass, Dil 2 29.50745 29.50745 29.50745 29.50745 29.50745 29.50745 29.50745 29.50762 29.50745 29.50745 29.50745
aliquot mass Dil1 (g) aliquot Dil 1 0.04966 0.04966 0.04966 0.04966 0.04966 0.04966 0.04966 0.04966 0.04983 0.04966 0.04966
dilute to mass (=D-1) (g) Dil. mass, Dil 1 29.31435 29.31435 29.31435 29.31435 29.31435 29.31435 29.31435 29.31435 29.31435 29.31452 29.31435
mass of 'unknown'mass RM
8017a 0.04776 0.04776 0.04776 0.04776 0.04776 0.04776 0.04776 0.04776 0.04776 0.04776 0.04793
MF Value, NNP RM 8017 5.381E+11 5.18E+11 5.57E+11 5.38E+11 5.35E+11 5.38E+11 5.38E+11 5.38E+11 5.36E+11 5.38E+11 5.36E+11
-2.00E+10 1.92E+10 -2.15E+07 -2.76E+09 1.60E+06 -1.20E+08 3.16E+06 -1.87E+09 3.18E+06 -1.94E+09 c i u i
Combined Standard Uncertainty, u c 2.8E+10 3.99E+20 3.69E+20 4.61E+14 7.61E+18 2.55E+12 1.44E+16 9.98E+12 3.50E+18 1.01E+13 3.78E+18 (c i u i )2
Degrees of Freedom, 7.31 50.9% 47.1% 0.00006% 0.97% 0.00000032% 0.00183% 0.0000013% 0.45% 0.0000013% 0.48% rel (c i u i )2
Coverage Factor, k 2.36 -1.40E+13 7.03E+08 -1.50E+09 -3.05E+12 9.21E+09 -6.92E+11 1.82E+10 -1.08E+13 1.84E+10 -1.12E+13 ci
Expanded Uncertainty, U 6.6E+10 aReconstituted with 1.986 g water
% Relative Expanded Uncertainty U r12.3%
Quantity Value + u i
Standard
Uncertainty, u i
21
Table 11. Kragten Spreadsheet for Determination of Particle Size of ‘Unknown’ AgNP Solution
aSee footnote a, Table 9.
u(ηnPS) u(INP AgNP) u(Idiss Ag) u(slopeAgionic) u(ρ Ag)
0.0014 11.81 0.03 21326.20 0.0064
Description
standard uncertainty of
the measured transport
efficiency (particle size
method) from Kragten
Spreadsheet
standard uncertainty of
the mean measured
intensity of 'unknown'
AgNPs composed of the
SE of four replicate runs
of RM 8017 added in
quadrature to the
estimated SE for
deadtime correctiona
standard uncertainty of
the mean measured
intensity of the dissolved
Ag background for four
individual vials of RM
8017
standard error of the
slope of the plot of IAg ionic
vs. massAg ionic as
computed using the
regression function of
Microsoft Excel
estimated standard
uncertainty for the
density of Ag from an
assumed rectangular
probability distribution of
magnitude 0.011 based
on variance of values
reported in the literature
degrees of freedom
i25.67 12.30 3.00 1.00 60.00
Quantity
Description
Quantity Name,
SymbolQuantity Value
transport efficiency
(particle size ηnPS0.03703 0.03845 0.03703 0.03703 0.03703 0.03703
intensity of the
particle events I NP AgNp 291.13 291.13 302.95 291.13 291.13 291.13
intensity of the
dissolved background Idiss Ag 0.4076 0.4076 0.4076 0.4340 0.4076 0.4076
slope of the
calibration curve RFAg ionic5276046.17 5276046.17 5276046.17 5276046.17 5297372.37 5276046.17
density of Agρ Ag
10.49 10.49 10.49 10.49 10.49 10.50
MF Value, d p RM 8017 71.89 72.80 72.85 71.88 71.79 71.87
9.12E-01 9.61E-01 -2.17E-03 -9.66E-02 -1.45E-02 c i u i
Combined Standard Uncertainty, u c 1.33 8.32E-01 9.23E-01 4.71E-06 9.33E-03 2.10E-04 (c i u i )2
Degrees of Freedom, 32.33 47.2% 52.3% 0.0% 0.5% 0.0% rel (c i u i )2
Coverage Factor, k 2.037 6.39E+02 8.13E-02 -8.24E-02 -4.53E-06 -2.28E+00 ci
Expanded Uncertainty, U 2.71
% Relative Expanded Uncertainty U r3.76%
Quantity Value + u i
Standard
Uncertainty, u i
22
13. Outcomes
13.1 spICP-MS time resolved intensity profile and particle size distribution of RM 8017
PVP-Coated Silver Nanoparticles – Nominal Core Diameter 75 nm
A typical time-resolved spICP-MS intensity profile and corresponding particle
size distribution for a dilute suspension of a single vial of RM 8017 are shown in
Figure 1. After reconstitution of the RM per instructions on the report of
investigation (ROI), the suspension was diluted with water 28-million fold (see
section 7.4) to a nominal particle number concentration of 1.7E04 g
-1, and measured
within 0.5 h of dilution. The intensity of each signal pulse is proportional to the
mass of analyte in a particle, and by assumption of a spherical shape, particle
diameter. The number of signal pulses is proportional to the particle number
concentration.
Ionic silver (Ag+), if present in the sample suspension, can be observed in a
spICP-MS time intensity profile as steady-state signal at the base of the signal
pulses formed by particles. An example is shown in Figure 2, which shows spICP-
MS results for a dilute AgNP suspension (2.5E04 g-1
, RM 8017) stored for 24 h at
room temperature. The instability of the AgNP suspension under these storage
conditions is evidenced by a smaller measured particle size, reduced particle
number concentration, and an increased mass fraction of ionic Ag.
13.2 Repeatability, reproducibility and comparability of spICP-MS Measurements
Results for the spICP-MS measurement of particle size, number
concentration and ionic mass fraction in eight vials of RM 8017 that demonstrate
the repeatability and reproducibility of the method are presented in Table 12. The
comparability of the spICP-MS particle size results with mean particle sizes
measured by TEM, atomic force microscopy (AFM), and ultra-small angle X-ray
scattering (USAXS) is illustrated in Figure 3. The comparability of spICP-MS
number concentration results with a derived number concentration value for RM
8017 is shown in Figure 4.
The spICP-MS measurements were performed in separate experiments (four
vials per experiment), conducted two years apart, and the presented results are
calculated using both the size and frequency based measure of transport efficiency.
Under repeatability conditions, a standard deviation of no greater than ± 1.4 nm
was observed for the nominally 75 nm AgNPs. Reproducibility conditions yielded
a similar standard deviation for the results using the size based measure of
transport efficiency, but results calculated using the frequency based measure of
transport efficiency showed a larger standard deviation (± 5.1 nm). The estimated
expanded uncertainty of the size measurement (see section 12.0 and example
Kragten spreadsheet in Table 11) ranged from ± 2.3 nm (3 % relative) using the
particle size-based measure of transport efficiency to ± 8.1 nm (± 14 % relative)
using the frequency-based measure of transport efficiency. The plot in Figure 3
shows that the particle size calculated using the frequency-based measure of
23
transport efficiency yields results that are lower than results using the size-based
measure of transport efficiency and in addition, are lower than the TEM value.
spICP-MS measured number concentration results show greater variability
and poorer comparability than the spICP-MS size measurements (see Table 12 and
Figure 4). Under repeatability conditions, standard deviations ranged from
± 1.9E10 g-1
(4 % relative) to ± 7.1E10 g-1
(10 % relative). Standard deviations
under reproducibility conditions were similar. Here again, differences in the results
calculated using the two measures of transport efficiency are observed, with the
frequency-based measure yielding results that deviated farthest from the reference
value. The reference value for RM 8017 was computed from the TEM measured
particle size, the value assigned mass of Ag in the vial, and assuming a
reconstitution mass of 2.000 g. Measured spICP-MS number concentrations using
the size-based measure of transport efficiency were in good agreement with the
computed number concentration reference value for RM 8017; however the
measured spICP-MS number concentrations using the frequency-based measure of
transport efficiency were biased high by 42 % to 55 %. This indicates that the
frequency-based measurement of transport efficiency is biased low, presumably
due to loss of AuNPs. Analysis of the total Au mass fraction via acid digestion of
a spICP-MS suspension diluted to 1.6E4 g-1
that was used to measure transport
efficiency did show that the measured Au mass fraction was significantly lower
than expected, indicating loss of Au to the container walls. A more rigorous study
of the stability of the very dilute suspension required for spICP-MS measurements
with respect to particle number concentration, is needed. It is worthy to note that
the size-based measurement of transport efficiency is more robust, as it is
unaffected by particle loss to the container walls.
The Ag ion content measured in each vial of RM 8017 and expressed as the
fraction of total Ag is listed in the last column of Table 12. It should be noted that
RM 8017 is not an ideal sample for measurement of the component Ag ion
content. Since RM 8017 is a freeze-dried material that is designed to be
reconstituted and used within as short time frame, a reference value for the Ag ion
content of RM 8017 has not been established. Furthermore due to the high AgNP
concentration and subsequent large dilution (nominally 28 million-fold) required to
achieve the optimum number concentration for single particle analysis, the ionic
Ag content, if any, has been so diluted that the measured signals are at the method
detection limit and subject to high uncertainty. This is evident in the observed
variability of the results. Measurement of the ionic fraction of a less concentrated
solution with respect to particle number, would presumably yield more consistent
results.
24
Table 12. Repeatability and Reproducibility of spICP-MS Measurements of Particle Size, Number Concentration and Ionic
Mass Fraction of RM 8017 PVP-Coated Silver Nanoparticles – Nominal Diameter 75 nm
Analysis
Date Vial#
Analysis
time, tanalysis
(s)
Number of
counted
particles,
CountNP
Particle Diameter, dP (nm) Particle Concentration, NP (g-1
) Ag Ionic
Fraction,
Agionic
(%)a
TE by size TE by
frequency TE by size
TE by
frequency
2013
1b 99.79 297 68.96 58.29 4.67E+11 7.73E+11 5.6
2c 179.70 275 68.24 58.19 4.39E+11 7.08E+11 7.0
3c 179.71 362 69.90 58.75 5.01E+11 8.08E+11 2.9
4c 179.75 256 70.32 59.97 4.02E+11 6.49E+11 1.2
Mean 69.1 58.8 4.52E+11 7.30E+11 4.2
SD 0.9 0.8 0.42E+11 0.71E+11 2.6
U 2.3 8.1 0.65E+11 2.3E+11
2015
5d 359.84 766 71.89 66.68 5.34E+11 6.69E+11 3.45
6d 359.78 675 71.52 66.35 4.87E+11 6.11E+11 3.78
7d 359.84 789 72.05 66.83 5.55E+11 6.95E+11 4.95
8d 359.83 846 69.00 64.00 5.77E+11 7.23E+11 5.01
Mean 71.1 65.97 5.38E+11 6.70E+11 4.30
SD 1.4 1.3 0.19E+11 0.24E+11 0.80
U 2.7 2.7 0.66E+11 1.1E+11
Reproducibility SD 1.4 5.1 0.61E+11 0.42E+11
Reference Value 74.6 ± 3.8e nm 4.75E+11 ± 0.68E+11
f
aExpressed as the fraction of total Ag
bNominal analysis NP, 2.4E04 g
-1,
cNominal analysis NP, 1.4E04 g
-1, dNominal analysis NP, 1.7E04 g
-1
eValue Assigned TEM size ± U for RM 8017
fDerived NP ± U for RM 8017 calculated based on TEM size, mass Ag in vial, and reconstitution mass of 2.000 g. Assumes all Ag is
particulate. U calculated via Kragten spreadsheet.
25
14 Abbreviations
AFM Atomic Force Microscopy
AgNPs Silver nanoparticles
AuNPs Gold nanoparticles
DI Deionized
Nano-EHS Environmental, Health and Safety as it pertains to nanomaterials
NNI National Nanotechnology Initiative
spICP-MS Single Particle Inductively Coupled Plasma Mass Spectrometry
TEM Transmission Electron Microscopy (TEM)
USAXS Ultra Small Angle X-ray Scattering
15 Acknowledgements
We would like to thank Debra Kaiser for her direction and vision in the coordination of the
implementation of the National Nanotechnology Initiative Nano-EHS research strategy at
the National Institute of Standards and Technology from which the idea for the
development of this series of protocols originated.
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27
Figure 1. Time-resolved intensity profile (A) and corresponding particle size distribution (B) for a spICP-MS suspension (1.7E04∙g
-1) of
a single vial of RM 8017, nominally 75 nm AgNPS measured within 0.5 h of dilution.
Figure 2. Time-resolved intensity profile (A) and corresponding particle size distribution (B) for a spICP-MS suspension (2.5E07
g
-1) of
AgNPS (RM 8017) stored at room temperature for 24 h. The instability of the dilute suspension under these conditions is
evidenced by a decrease in measured particle size and number concentration, and an increase in the mass fraction of ionic Ag.
28
Figure 3. Comparability of the spICP-MS particle size results for RM 8017 calculated using both the size-based
and frequency-based measure of transport efficiency with mean particle sizes measured by TEM, AFM,
and USAXS